Similar to [1]}, to deal with possible overlaps in the IFSs, we shall first apply the CP-chain method at the symbolic space level, then we map the CP-chain to the Euclidean space through the canonical mappings \(\Phi _{\mathbf {I}}\)  and \(\Phi _{\mathbf {J}}\) . For IFSs with different contraction ratios \(\delta \)  and \(\rho \)  (an affine case), the underlining dynamical system is the product space
\(X=\mathbb {T}\times \Sigma _a\times \Sigma _b\) 
